Review of research on high-speed railway subgrade settlement in soft soil area

Abstract

Construction issues of high-speed rail infrastructures have been increasingly concerned worldwide, of which the subgrade settlement in soft soil area becomes a particularly critical problem. Due to the high compressibility and low permeability of soft soil, the post-construction settlement of the subgrade is extremely difficult to control in these regions, which seriously threatens the operation safety of high-speed trains. In this work, the significant issues of high-speed railway subgrades in soft soil regions are discussed. The theoretical and experimental studies on foundation treatment methods for ballasted and ballastless tracks are reviewed. The settlement evolution and the settlement control effect of different treatment methods are highlighted. Control technologies of subgrade differential settlement are subsequently briefly presented. Settlement calculation algorithms of foundations reinforced by different treatment methods are discussed in detail. The defects of existing prediction methods and the challenges faced in their practical applications are analyzed. Furthermore, the guidance on future improvement in control theories and technologies of subgrade settlement for high-speed railway lines and the corresponding challenges are provided.

References

[1.] Wang BL, Yang XW, Zhou Y . Subgrade and track engineering of high speed railway 2015 Shanghai Tongji University Press(in Chinese)

[2.] National Railway Administration. Code for design of high speed railway (TB10621-2014) 2014 Beijing China Railway Press(in Chinese)

[3.] Guo Y, Zhai WM, Sun Y. A mechanical model of vehicle–slab track coupled system with differential subgrade settlement. Struct Eng Mech 2018, 66 1 15-25

[4.] Guo Y, Zhai WM. Long-term prediction of track geometry degradation in high-speed vehicle–ballastless track system due to differential subgrade settlement. Soil Dyn Earthq Eng 2018, 113 1-11

[5.] Zhai WM, Zhao CF, Xia H . Basic scientific issues on dynamic performance evolution of the high-speed railway infrastructure and its service safety. Sci Sin (Technol) 2014, 44 7 645-660 in Chinese)

[6.] Gong XN. Application of composite foundation theory and engineering 2002 Beijing China Construction Industry Press(in Chinese)

[7.] Biot MA. Theory of elasticity and consolidation for a porous anisotropic solid. J Appl Phys 1955, 26 2 182-185

[8.] Wang X (2006) Prediction and control of settlement of high speed railway soft subgrade treated with cement powder mixing piles. Dissertation of Ph.D., Tongji University, Shanghai (in Chinese)

[9.] Zhou SH (2003) Experimental research on control methods on settlements of subgrade and bridge pile. Research Report, Tongji University, Shanghai (in Chinese)

[10.] Yin ZZ. Status and prospects of soil mechanics development. J Hohai Univ 1999, 27 1 1-5

[11.] Liu HL, Zhao MH. Review of ground improvement technical and its application in China. China Civ Eng J 2016, 49 1 96-115(in Chinese)

[12.] Barron RA. Consolidation of fine-grained soils by drain wells. Trans Am Soc Civ Eng 1948, 113 1 718-742

[13.] Yoshikuni H, Nakanodo H. Consolidation of soils by vertical drain wells with finite permeability. Soils Found 1974, 14 2 35-46

[14.] Zhu GF, Yin JH. Consolidation of soil with vertical and horizontal drainage under ramp load. Géotechnique 2001, 51 4 361-367

[15.] Leo CJ. Equal strain consolidation by vertical drains. J Geotech Geoenviron Eng 2004, 130 3 316-327

[16.] Walker R, Indraratna B. Consolidation analysis of a stratified soil with vertical and horizontal drainage using the spectral method. Géotechnique 2009, 59 5 439-449

[17.] Lu MM, Xie KH, Wang SY. Consolidation of vertical drain with depth-varying stress induced by multi-stage loading. Comput Geotech 2011, 38 8 1096-1101

[18.] Lei GH, Zheng Q, Wang CW . An analytical solution for consolidation with vertical drains under multi-ramp loading. Géotechnique 2015, 65 7 531-547

[19.] Ho L, Behzad F. Analytical solution for the two-dimensional plane strain consolidation of an unsaturated soil stratum subjected to time-dependent loading. Comput Geotech 2015, 67 1-16

[20.] Indraratna B, Kan ME, Potts D . Analytical solution and numerical simulation of vacuum consolidation by vertical drains beneath circular embankments. Comput Geotech 2016, 80 83-96

[21.] Lu MM, Sloan SW, Indraratna B . A new analytical model for consolidation with multiple vertical drains. Int J Numer Anal Methods Geomech 2016, 40 1623-1640

[22.] Tian Y, Wu WB, Jiang GS . Analytical solutions for vacuum preloading consolidation with prefabricated vertical drain based on elliptical cylinder model. Comput Geotech 2019, 116 103202

[23.] Jang WY, Chung SG. Long-term settlement analysis of partially improved thick clay deposit. Geotext Geomembr 2014, 42 6 620-628

[24.] Yuan S, Zhong H. Consolidation analysis of non-homogeneous soil by the weak form quadrature element method. Comput Geotech 2014, 62 1-10

[25.] Chai JC, Shen JSL, Liu MD . Predicting the performance of embankments on PVD-improved subsoils. Comput Geotech 2018, 93 222-231

[26.] Wang GC. Consolidation of soft clay foundations reinforced by stone columns under time-dependent loadings. J Geotech Geoenviron Eng 2009, 135 12 1922-1931

[27.] Lu MM, Xie KH, Wang SY . Analytical solution for the consolidation of a composite foundation reinforced by an impervious column with an arbitrary stress increment. Int J Geomech 2013, 13 1 33-40

[28.] Yang T, Yang JZ, Ni J. Analytical solution for the consolidation of a composite ground reinforced by partially penetrated impervious columns. Comput Geotech 2014, 57 30-36

[29.] Liu KW, Rowe RK. Numerical study of the effects of geosynthetic reinforcement viscosity on behaviour of embankments supported by deep-mixing-method columns. Geotext Geomembr 2015, 43 6 567-578

[30.] Wonglert A, Jongpradist P. Impact of reinforced core on performance and failure behavior of stiffened deep cement mixing piles. Comput Geotech 2015, 69 93-104

[31.] Long PV, Nguyen LV, Bergado DT . Performance of PVD improved soft ground using vacuum consolidation methods with and without airtight membrane. Geotext Geomembr 2015, 43 6 473-483

[32.] Bergado DT, Long PV, Chaiyaput S et al (2018) Prefabricated vertical drain (PVD) and deep cement mixing (DCM)/stiffened DCM (SDCM) techniques for soft ground improvement. In: Bui QB, Cajka R, Tran MT, Trinh TA, Yasar AUH, Wets G, Woloszyn M (eds) IOP conference series: earth and environmental science, 2nd international conference on sustainable development in civil, urban and transportation engineering (CUTE 2018), vol 143, pp 1–31. IOP Publishing, Bristol

[33.] Chai JC, Rondonuwu SG. Surcharge loading rate for minimizing lateral displacement of PVD improved deposit with vacuum pressure. Geotext Geomembr 2015, 43 6 558-566

[34.] Wang J, Cai YQ, Fu HT . Experimental study on a dredged fill ground improved by a two-stage vacuum preloading method. Soils Found 2018, 58 3 766-775

[35.] Shen SL, Han J, Du YJ. Deep mixing induced property changes in surrounding sensitive marine clays. J Geotech Geoenviron Eng 2008, 134 6 845-854

[36.] Liu SY, Du YJ, Yi YL . Field investigations on performance of T-shaped deep mixed soil cement column-supported embankments over soft ground. J Geotech Geoenviron Eng 2012, 138 6 718-727

[37.] Wang BL, Yang LC, Gong QM . Experimental study on soft soil reinforced by vacuum combined with fill preloading. J Tongji Univ (Nat Sci) 2006, 34 4 499-503(in Chinese)

[38.] China Railway Fourth Survey and Design Institute Group Co., Ltd. Evaluation on calculation methods of soft subgrade settlement treated with different reinforced measures 2005 Wuhan China Railway Fourth Survey and Design Institute Group Co., Ltd(in Chinese)

[39.] Cai DG, Ye YS, Zhang QL . Field test study on the mechanical behaviors of the geosynthetic-reinforced pile-supported embankment and the deformation of the reinforced bedding. China Railw Sci 2009, 30 5 1-8(in Chinese)

[40.] Bouassida M, Buhan PD, Dormieux L. Bearing capacity of a foundation resting on a soil reinforced by a group of columns. Géotechnique 1995, 45 1 25-34

[41.] Castro J, Sagaseta C. Consolidation around stone columns. Influence of column deformation. Int J Numer Anal Methods Geomech 2009, 33 7 851-877

[42.] Castro J, Sagaseta C. Consolidation and deformation around stone columns: numerical evaluation of analytical solutions. Comput Geotech 2011, 38 3 354-362

[43.] Castro J, Sagaseta C. Deformation and consolidation around encased stone columns. Geotext Geomembr 2011, 29 3 268-276

[44.] Huang J, Han J. 3D coupled mechanical and hydraulic modeling of a geosynthetic-reinforced deep mixed column-supported embankment. Geotext Geomembr 2009, 27 4 272-280

[45.] Zhang J, Zheng JJ, Chen BG . Coupled mechanical and hydraulic modeling of a geosynthetic reinforced and pile-supported embankment. Comput Geotech 2013, 52 28-37

[46.] Zhuang Y, Wang KY, Liu HL. A simplified model to analyze the reinforced piled embankments. Geotext Geomembr 2014, 42 2 154-165

[47.] Bhasi A, Rajagopal K. Numerical study of basal reinforced embankments supported on floating/end bearing piles considering pile soil interaction. Geotext Geomembr 2015, 43 6 524-536

[48.] Yu Y, Bathurst RJ, Damians IP. Modified unit cell approach for modelling geosynthetic-reinforced column-supported embankments. Geotext Geomembr 2016, 44 3 332-343

[49.] Zhao LS, Zhou WH, Yuen KV. A simplified axisymmetric model for column supported embankment systems. Comput Geotech 2017, 92 96-107

[50.] Yu Y, Bathurst RJ. Modelling of geosynthetic-reinforced column-supported embankments using 2D full-width model and modified unit cell approach. Geotext Geomembr 2017, 45 2 103-120

[51.] Huang ZY, Ziotopoulou K, Filz GM. 3D numerical limiting case analyses of lateral spreading in a column-supported embankment. J Geotech Geoenviron Eng 2019, 145 11 04019096

[52.] Xie KH, Lu MM, Hu AF . A general theoretical solution for the consolidation of a composite foundation. Comput Geotech 2009, 36 1–2 24-30

[53.] Chen RP, Xu ZZ, Chen YM . Field tests on pile-supported embankments over soft ground. J Geotech Geoenviron Eng 2010, 136 6 777-785

[54.] Hong WP, Hong S, Song JS. Load Transfer by Punching Shear in Pile-Supported Embankments on Soft Grounds. Mar Georesour Geotechnol 2011, 29 4 279-298

[55.] Jiang GL, Liu XF, Zhang JW . Shaking table test of composite foundation reinforcement of saturated silty soil ground for high speed railway. J Southwest Jiaotong Univ 2006, 41 2 190-196(in Chinese)

[56.] Briançon L, Simon B. Performance of pile-supported embankment over soft soil: full-scale experiment. J Geotech Geoenviron Eng 2012, 138 4 551-561

[57.] Xing HF, Zhang Z, Liu HB . Large-scale tests of pile-supported earth platform with and without geogrid. Geotext Geomembr 2014, 42 6 586-598

[58.] Wang CD, Wang BL, Guo PJ . Experimental analysis on settlement controlling of geogrid-reinforced pile-raft-supported embankments in high-speed railway. Acta Geotech 2015, 15 9 231-242

[59.] Fagundes DF, Almeida MSS, Thorel L . Load transfer mechanism and deformation of reinforced piled embankments. Geotext Geomembr 2017, 45 2 1-10

[60.] McGuire MP, Filz GM. Bench-scale test apparatus for modeling column-supported embankments. Geotech Test J 2017, 40 5 731-745

[61.] Zhang Z, Ye GB, Cai YY . Centrifugal and numerical modeling of stiffened deep mixed column-supported embankment with slab over soft clay. Can Geotech J 2019, 56 10 1418-1432

[62.] Zheng G, Jiang Y, Han J . Performance of cement-fly ash-gravel pile-supported high-speed railway embankments over soft marine clay. Mar Georesour Geotechnol 2011, 29 2 145-161

[63.] Miranda M, Costa AD, Castro J . Influence of geotextile encasement on the behaviour of stone columns: laboratory study. Geotext Geomembr 2017, 45 1 14-22

[64.] China Railway Design Group Co., Ltd (2009) Experimental research on settlements of high speed railway subgrade reinforced with CFG piles. Research Report, China Railway Design Group Co., Ltd, Tianjin (in Chinese)

[65.] National Railway Administration. Technical code for ground treatment of railway engineering (TB10106-2010) 2010 Beijing China Railway Press(in Chinese)

[66.] Galvín P, Domínguez J. High-speed train-induced ground motion and interaction with structures. J Sound Vib 2007, 307 3–5 755-777

[67.] Shan Y, Albers B, Savidis SA. Influence of different transition zones on the dynamic response of track-subgrade systems. Comput Geotech 2013, 48 21-28

[68.] Shan Y, Shu Y, Zhou SH. Finite-infinite element coupled analysis on the influence of material parameters on the dynamic properties of transition zones. Constr Build Mater 2017, 148 548-558

[69.] Varandas JN, Hölscher P, Silva MAG. Three-dimensional track–ballast interaction model for the study of a culvert transition. Soil Dyn Earthq Eng 2016, 89 116-127

[70.] Mishra D, Qian Y, Huang H . An integrated approach to dynamic analysis of railroad track transitions behavior. Transp Geotech 2014, 1 4 188-200

[71.] Faragau AB, Metrikine AV, van Dalen KN. Transition radiation in piecewise-linear and infinite one-dimensional structure—a Laplace transform method. Nonlinear Dyn 2019, 98 4 2435-2461

[72.] Shi C, Zhao C, Zhang X . Analysis on dynamic performance of different track transition forms using the discrete element/finite difference hybrid method. Comput Struct 2020, 230 1-11

[73.] Read D, Li D (2006) Design of track transitions. Research Results Digest 79, Transit Cooperative Research Program, Transportation Research Board, National Academies

[74.] Mishra D, Tutumluer E, Kazmee H et al (2014) Use of multi-depth deflectometers and strain gauges to investigate the differential movement at railway bridge approaches. In: Pombo J (ed) Proceedings of the second international conference on railway technology: research, development and maintenance. Civil-Comp Press; Paper 229

[75.] Varandas JN, Hölscher P, Silva MAG. Settlement of ballasted track under traffic loading: application to transition zones. Proc IMechE Part F J Rail Rapid Transit 2014, 228 3 242-259

[76.] Hu YF, Li NF. Theory of ballastless track-subgrade for high speed railway 2010 Beijing China Railway Publishing House(in Chinese)

[77.] Li DQ, Hyslip J, Sussmann T . Railway geotechnics 2016 Boca Raton CRC Press, Taylor & Francis Group

[78.] Xiao JH, Wang BL, Wang CD . Differential settlement of subgrade and its control for high speed railway 2015 Shanghai Tongji University Press(in Chinese)

[79.] Indraratna B, Rujikiatkamjorn C, Sathananthan I. Analytical and numerical solutions for a single vertical drain including the effects of vacuum preloading. Can Geotech J 2005, 42 4 994-1014

[80.] Mohamedelhassan E, Shang J. Vacuum and surcharge combined onedimensional consolidation of clay soils. Can Geotech J 2002, 39 5 1126-1138

[81.] Yapage NNS, Liyanapathirana DS. A parametric study of geosynthetic-reinforced column-supported embankments. Geosynth Int 2014, 21 3 213-232

[82.] Liu KW, Rowe RK. Numerical modelling of prefabricated vertical drains and surcharge on reinforced floating column-supported embankment behaviour. Geotext Geomembr 2015, 43 6 493-505

[83.] Filz GM, Sloan JA, McGuire MP . Settlement and vertical load transfer in column-supported embankments. J Geotech Geoenviron Eng 2019, 145 10 04019083

[84.] Phutthananon C, Jongpradist P, Jamsawang P. Influence of cap size and strength on settlements of TDM-piled embankments over soft ground. Mar Georesour Geotechnol 2019

[85.] Chen Y, Huang B, Chen Y. Reliability analysis of high level backfill based on chaotic optimization. Chin J Geotech Eng 2008, 30 5 764-768(in Chinese)

[86.] Xu MJ, Ni PP, Mei GX . Time effects on settlement of rigid pile composite foundation: simplified models. Int J Comput Methods 2018, 15 1 1850066

[87.] Li L, Li JP, Sun DA, Gong WB. Semi-analytical approach for time-dependent load-settlement response of a jacked pile in clay strata. Can Geotech J 2017, 54 12 1682-1692

[88.] Wang BL, Yang LC, Zhou SH . Experimental study on the settlement control of high-speed railway subgrade over deep soft clay reinforced by CFG piles. J China Railw Soc 2006, 28 6 112-116(in Chinese)

[89.] Lam LG, Bergado DT, Voottipruex P et al (2014) Performance of PVDs improvement with and without vacuum preloading for soft ground. In: Proceedings of the 9th international symposium on lowland technology, Japan, pp 313–317

[90.] Hewlett WJ, Randolph MA. Analysis of piled embankments. Ground Eng 1988, 21 3 12-18

[91.] Zaeske D (2001) On the effect of unreinforced and reinforced mineral base courses over pile-like foundation elements. Schriftenreihe Geotechnik. Dissertation, Universität Kassel (in German)

[92.] BS8006-1. Code of practice for strengthened/reinforced soils and other fills 2010 London British Standards Institution

[93.] Rogbeck Y, Alén C, Franzén G . Nordic guidelines for reinforced soils and fills 2003 Shanghai Nordic Geosynthetic Group of the Nordic Geotechnical Societies, Nordic Industrial Fund

[94.] Railway Institute of Integrated Technology. Design and construction guide for mixing foundation (mechanical mixing mode) 2001 Tokyo Institute of Integrated Railway Technology(in Japanese)

[95.] The German Geotechnical Society (DGGT). Recommendations for design and analysis of earth structures using geosynthetic reinforcements—EBGEO (DGGT/recommendations) embankments on soft soils 2011 Hoboken Ernst & Sohn

[96.] Spangler MG, Handy RL. Soil Engineering 1973 New York Intext Educational Publishers

[97.] van Eekelen SJM, Bezuijen A, van Tol AF. An analytical model for arching in piled embankments. Geotext Geomembr 2013, 39 78-102

[98.] van Eekelen SJM, Bezuijen A, van Tol AF. Validation of analytical models for the design of basal reinforced piled embankments. Geotext Geomembr 2015, 43 1 56-81

[99.] van Eekelen SJM, Vollmert L (2018) The design guideline basal reinforced piled embankments; the Dutch CUR226: 2016 and the German EBGEO: 2010; a comparison of design models and safety approaches. In: Proceedings of 11 ICG, Korea

[100.] Han GX, Gong QM, Zhou SH. Soil arching in a piled embankment under dynamic load. Int J Geomech 2015, 15 6 04014094

[101.] Bi ZQ, Gong QM, Zhou SH . Shakedown analysis of soil arch in piled embankment of high-speed railway. J China Railw Soc 2016, 38 11 102-110(in Chinese)

[102.] Zhuang Y, Cheng X, Wang K. Analytical solution for geogrid-reinforced piled embankments under traffic loads. Geosynth Int 2019

[103.] Lu W, Miao L. A simplified 2-D evaluation method of the arching effect for geosynthetic-reinforced and pile-supported embankments. Comput Geotech 2015, 65 97-103

[104.] Feng SJ, Ai SG, Chen HX. Estimation of arching effect in geosynthetic-reinforced structures. Comput Geotech 2017, 87 188-197

[105.] Rui R, van Tol F, Xia YY . Evolution of soil arching: 2D analytical models. Int J Geomech 2018, 18 6 04018056

[106.] Zhang C, Jiang G, Liu X . Arching in geogrid-reinforced pile-supported embankments over silty clay of medium compressibility: field data and analytical solution. Comput Geotech 2016, 77 11-25

[107.] Wang CD, Wang BL, Zhou SH . Calculation method of settlement of rigid pile-geogrid composite foundation of high-speed railways and comparisons with measured data. J China Railw Soc 2013, 35 8 80-87(in Chinese)

[108.] National Railway Administration. Code for design on subsoil and foundation of railway bridge and culvert (TB10093-2017) 2017 Beijing China Railway Press(in Chinese)

[109.] Chik Z, Aljanabi QA, Kasa A . Tenfold cross validation artificial neural network modeling of the settlement behavior of a stone column under a highway embankment. Arab J Geosci 2014, 7 11 4877-4887

[110.] Qi CQ, Wu QB, Shi B . Application of BP neural network on deformation prediction for permafrost embankment. Hydrogeol Eng Geol 2007, 34 4 27-30

[111.] Feng Z, Xu ZY, Wang LJ . Grey Prediction of embankment settlement and its application. J North Jiaotong Univ 2004, 27 4 23-26(in Chinese)

[112.] Du YL, Lai J, Liu XF. Grey prediction model for construction settlement forecast of embankment of high-speed railway and its application. J Railw Sci Eng 2009, 6 1 36-40(in Chinese)

[113.] Wei K, Gong QM, Zhou SH. Ant colony algorithms of long-term uneven settlement prediction in tunnel. Journal of Tongji University (Natural Science) 2009, 37 8 993-998(in Chinese)

[114.] Wei K, Gong QM, Zhou SH. Forecast of long-term settlement of metro tunnel on the basis of ant colony optimization. J China Railw Soc 2008, 30 4 79-83(in Chinese)

[115.] Tan TS, Inoue T, Lee SL. Hyperbolic method for consolidation analysis. J Geotech Eng ASCE 1991, 117 11 1723-1737

[116.] Tan SA, Chew SH. Comparison of the hyperbolic and Asaoka observational method of monitoring consolidation with vertical drains. Soils Found 1996, 36 3 31-42

[117.] Chen SX, Wang XY, Xu XC . Three-point modified exponential curve method for predicting subgrade settlements. Rock Soil Mech 2011, 32 11 3355-3360

[118.] Wang W, Sun BX, Lu TH. 3-parameter prediction model of post-construction settlement for soft soil foundation under highway embankment. China J Highw Transp 2008, 21 2 12-17(in Chinese)

[119.] Hoshino K. The latest problems on soils and foundations. J Japan Soc Civil Eng 1962, 47 7 63-67(in Japanese)

[120.] Asaoka A. Observational procedure of settlement prediction. Soils Found 1978, 18 4 87-101

[121.] Asaoka A. An inverse problem approach to settlement prediction of multi-dimensional condition behavior. Soils Found 1984, 24 1 49-62

[122.] Engineering Management Center of the Ministry of Railways. Technical manual for deformation observation and evaluation of passenger dedicated railways 2009 Beijing China Railway Press(in Chinese)

[123.] Dafalias YF. Bounding surface plasticity (I): mathematical formulation and hypoplasticity. J Eng Mech ASCE 1986, 112 9 966-987

[124.] Prevost JH. A simple plasticity theory for frictional cohesionless soils. Int J Soil Dyn Earthq Eng 1985, 4 1 9-17

[125.] Zienkiewicz C, Leung KH, Pastor M. Simple model for transient soil loading in earthquake analysis (I): basic model and its application. Int J Numer Anal Methods Geomech 1985, 9 5 453-476

[126.] Suiker SJ, Borst R. A numerical model for the cyclic deterioration of railway tracks. Int J Numer Methods Eng 2003, 57 4 441-470

[127.] Dahlberg T. Some railroad settlement models—a critical review. Proc IMechE Part F J Rail Rapid Transit 2001, 215 4 289-300

[128.] Shenton M. Ballast deformation and track deterioration 1985 London Track Technology. Thomas Telford Ltd 253-265

[129.] Sato Y. Japanese studies on deterioration of ballasted track. Vehicle Syst Dyn 1995, 24 Supplement 197-208

[130.] Iwnicki S, Grassie S, Kik W. Track settlement prediction using computer simulation tools. Vehicle Syst Dyn 2000, 33 Supplement 2-12

[131.] Office for Research and Experiments of the International Union of Railways (ORE) (1988) Dynamic vehicle/track interaction phenomena, from the point of view of track maintenance. Question D161, RP3

[132.] Monismith CL, Ogawa N, Freeme CR. Permanent deformation characteristics of subgrade soils due to repeated loading. Transp Res Rec 1975, 537 1-17

[133.] Li DQ, Selig ET. Cumulative plastic deformation for tine grained subgrade soils. J Geotech Eng 1996, 122 12 1006-1013

[134.] Chai JC, Miura N. Traffic-load-induced permanent deformation of road on soft subsoil. J Geotech Geoenviron Eng 2002, 128 11 907-916

[135.] Liu JK, Xiao JH. Experimental study on the stability of railroad silt subgrade with increasing train speed. J Geotech Geoenviron Eng 2010, 136 6 833-841

[136.] Bian XC, Jiang HG, Chen YM. Accumulative deformation in railway track induced by high-speed traffic loading of the trains. Earthq Eng Eng Vib 2010, 9 3 319-326

[137.] Dong L, Cai D, Ye Y . A method for predicting the cumulative deformation of high-speed railway subgrades under cyclic train loads. China Civ Eng J 2010, 43 6 100-108(in Chinese)

[138.] Vale C, Calçada R. A dynamic vehicle–track interaction model for predicting the track degradation process. J Infrastruct Syst 2014, 20 3 1-13

[139.] Mauer L. An interactive track–train dynamic model for calculation of track error growth. Vehicle Syst Dyn 1995, 24 Supplement 209-221

[140.] Ford R. Differential ballast settlement, and consequent undulations in track, caused by vehicle–track interaction. Vehicle Syst Dyn 1995, 24 Supplement 222-233

[141.] Wang HY, Markine V. Modelling of the long-term behaviour of transition zones: prediction of track settlement. Eng Struct 2018, 156 294-304

[142.] Shan Y, Zhou SH, Zhou HC . Iterative method for predicting uneven settlement caused by high-speed train loads in transition-zone subgrade. Transp Res Rec J Transp Res Board 2017, 2607 7-14

[143.] China Railway Design Corporation. Research report of comprehensive application of CFG pile composite foundation in high-speed railway and the field experiment of LiYao test section 2009 Tianjin China Railway Design Corporation(in Chinese)